So every year my wife watches Christmas in Connecticut. Early on in the movie one of the military guys tells the other the way to get what he wants from a nurse is to "give her the old magoo". As sexually euphemistic as it sounds, I'm pretty sure it's just meaning "feed her a line of crap". However I can't seem to find any other use of the term anywhere. Is my guess on the meaning correct and was this a popular phrase at the time?

Little White Lies
While Connecticut's premise hinges on Elizabeth's literary license, almost every main character can be blamed for some dishonest representation. All of the harmless lies collide to cause the commotion that ends up being the Christmas holiday on the Connecticut farm. Lacking a villain, as well as any malicious intent, the misrepresentation (or "The Magoo" as one minor character calls it) creates the conflict of the story.

In the 1945 Barbara Stanwyck film "Christmas in Connecticut," a "magoo' is a seductive, complex story you tell to get what you want.
He gave her "the magoo" by saying he couldn't marry her because he was going to die in 2 months.

... I can't seem to find any other use of the term anywhere. ...was this a popular phrase at the time?

I don't think it was too popular. At least it's difficult to find anything on the web amid the avalanche of Mr. Magoo cartoon shorts references. You can't even narrow your search with "Christmas," for Christmas in Connecticut, since there is apparently a Mr. Magoo Christmas movie that brings another thousand pages of crap into the search.

But here's an odd one, an article titled "The Magoo," from Time, July 26, 1943, not even on the web but cached by Google here:

Quote:

Monday, Jul. 26, 1943
The Magoo
To all appearances, it was a routine press conference at Allied headquarters in North Africa. General Eisenhower spoke casually of the overall military picture. He was in good form, smiling, crinkling his forehead, moving his eyes swiftly from face to face. It was the middle of June. Then the General said quietly: Overseas operations will begin within a month. Objective: Sicily.

This was it. The correspondents felt themselves tighten up. The General was not smiling now; his icy blue eyes moved from one to another of the reporters. None of them had expected the top Allied commander to take them so intimately, so significantly into his confidence. The General warned them that they must not talk.

They Fly Through the Air. For days thereafter the 100-odd American and British correspondents in North Africa went about with the guilty demeanor of men bursting with a secret. When they had to refer to it, they called it "the magoo," "that thing," or just "it." This was what they had trained for. Some veterans had been almost four years around the front lines. Others had studied invasions at service schools in Britain. One and all, they kept the secret.